Harry Partch related scales

The famous Partch scale is his 43 note Genesis or "pure" scale. The Wikipedia article on it is here, and the scale itself here. Other Partch scales are his 29-note adapted viola scale, his 37-note draft exposition scale, his 41 note exposition scale and his 43-note exposition scale.

By removing 11/10 and 20/11 from the Genesis scale, we obtain a 41 note epimorphic scale which has been called Genesis Minus; this scale is close to being a Fokker block, tempering to a MOS in cassandra, magic and rodan temperaments, for each of which the generators range from -20 to 20, leading to a symmetrical scale. Paul Erlich constructed this Fokker block which is also a MOS in octacot temperament, with generator range -20 to 20. By chosing other linearly independent temperaments supported by the 11-limit patent val for 41edo to add to cassandra, magic and rodan and requiring the range of generators to be -20 to 20 for that temperament also, we can find other alternatives to Genesis Minus based on monkey, superkleismic, or miracle, which do equally well measured by differences from Genesis Minus.

A 58 note scale is as small as is possible for an epimorphic scale containing Genesis, for example this one. By way of comparison, here is a Fokker block containing 35 of the 43 notes of Genesis: mynadiaechhemi. Mynadiaechhemi also contains a complete 11-limit tonality diamond, and 58 is the smallest size of epimorphic scale for which that is possible

see also Harry Partch